Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Time series analysis., how is a free hand graph secular trend method plotte...

how is a free hand graph secular trend method plotted

Caveat, Caveat We must be careful when interpreting the meaning of asso...

Caveat We must be careful when interpreting the meaning of association. Although two variables may be associated, this association does not imply that variation in the independ

Ryan-joiner - normal probability plot, The Null Hypothesis - H0:  The rando...

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

Assumptions in anova, Assumptions in ANOVA The various populations f...

Assumptions in ANOVA The various populations from which the samples are drawn should be normal and have the same variance. The requirement of normality can be discarded if t

Find out the probability, There are n seats on an airplane and n passengers...

There are n seats on an airplane and n passengers have bought tickets. Unfortunately, the first passenger to enter the plane has lost his ticket and, so he just chooses a seat at r

Explain ridge regression, Using log(x1), log(x2) and log(x3) as the predict...

Using log(x1), log(x2) and log(x3) as the predictors, do pair wise scatterplots of all pairs of variables (including the response) and comment (use the pairs function). Do you thin

Muti linear regression model problem, Muti linear regression model problem ...

Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school

Kolmogorov-smirnov - normal probability plot, The Null Hypothesis - H0:  Th...

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

Weighted arithmetic mean, Weighted Arithmetic Mean Another aspect...

Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd